Re: How many different unit fractions are lessorequal than all unit fractions?

On 24.09.2024 22:19, Jim Burns wrote:

On 9/24/2024 3:28 PM, WM wrote:

Thus
increasing NUF(x) from 0 to infinity
WITH intermediate steps
is gibberish,

The only alternative would by infinitely many unit fractions at one point. That is not gibberish but wrong.

 Of many suitable definitions of natural numbers,
one is:
they are well.ordered (subsets minimummed or empty)
they continue (have successors)
they are reached by a step (≠0 have predecessors)
 The natural numbers are our Paradigm of Finite.
 There is no first unreachable natural number.

The natural numbers n belonging to the first infinitely many unit fractions 1/n, i.e. there where NUF(x) increases at one point from 0 to infinity, cannot be distinguished in your opinion. Thus they are unreachable.

By that and by its well.order,
there is no unreachable natural number.
 ω is not a natural number.
⎛ Each before ω can be reached.
⎝ Each which can be reached is before ω.
 If ω-1 existed such that (ω-1)+1 = ω
then ω could be reached

If ω-1 could be seen. But it cannot.
Regards, WM